1. The document discusses the concept of mode in statistics, including definitions, methods of computing mode in individual, discrete, and grouped series, merits and demerits, and uses. 2. Key methods discussed include computing mode by inspection when values are small, making discrete or grouped series when values are large, and using the formula Mode = 3Median - 2Mean. 3. The mode is the value that occurs most frequently in a data set and indicates the central tendency. It is useful when wanting a representative typical value.

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DR. R.K. RAO (PRINCIPAL)
GUIDED BY - SHEETAL GUPTA
PRESENTED BY..
NIKITA DEWANGAN
M.Sc.2ND SEMESTER
BIOTECHNOLOGY
G.D. RUNGTA COLLEGE OF SCIENCE & TECHNOLOGY
KOHKA-KURUD,BHILAI DURG (C.G.)

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 INTRODUCTION
 DEFINITION
 METHODS OF COMPUTING MODE IN INDIVIDUAL SERIES
 METHODS OF COMPUTING MODE IN DISCRETE SERIES
 METHODS OF COMPUTING MODE IN GROUP SERIES
 MERITS
 DEMERITS
 USES
 REFRENCES

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 The word mode is made from the French language LaMode , which means
fashion or system.
 The value of the variable for which the frequency is maximum is called
mode or modal value and is denoted by Z or Mo.

4.  Mode is defined as the value of maximum frequency. If each value occurs only
once then there is no mode or all the values are modes.
If there are two or more values with maximum frequency, there may be two or
more modes. Such frequency distribution is called multi modal.
Thus a frequency distribution with two modes is called bimodal with three
modes is called trimodal.
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5.  BY INSPECTION :- When the number of the observation is small mode is
obtained at a glance by looking which one of the observations occurs most
frequenty.
 BY MAKING DISCRETE SERIES OR GROUPED SERIES:- When the
number of observation is large convert the individual series into discrete or
grouped series and locate mode accordingly.
 WITH HELP OF MEAN AND MEDIAN :- Using the empirical formula.
Mode = 3 Median - 2 Mean
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6.  ILLUSTRATION(1)
 The following data shows the ages of 20 students in a class find the mode ;-
15 ,17,18,20,22,24,21,17,16,15,21,22,23,22,17,22,18,22,19, 20
Solution :- place the number in ascending order :-
15,15,16,17,17,17,18,18,19,20,20,21,21,22,22,22,22,22,23,24
 22 → 5 times present in series
 Obsviously 22 years age belong to maximum number of students. Hence
 Mode is 22 year.
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7.  The discrete series for the given data is as follows :-
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X F
15 → 2
16 → 1
17 → 3
18 → 2
19 → 1
20 → 2
21 → 2
22 → 5
23 → 1
24 → 1

8.  ILLUSTRATION (2)
 The following are the marks obtained by biotech student find the mode:-
2,0,9,15,11,17,19,21,22,23,25,26,27,28,31,32,33,34,35,45
Solution : - arrange the values in ascending order :-
0,2,9,11,15,17,19,21,22,23,25,26,27,28,31,32,33,34,35,45
Since each value occurs once there is no mode or all the values are mode.
However we can find the mode using the empirical formula ;
Mode = 3 Median – 2 Mean
Arithimatic mean of these values;
X = ∑X / N
= 455 / 20
= 22.75
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9.  Median of these values;
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M = 10th value + 11th value
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M = 10th value + 11th value
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2
= 24
Mode = 3 Median - 2 Mean
= 3 × 24 - 2 × 22.75
= 26.50
MODE

10. 1. BY INSPECTION
2. BY GROUPING
1. BY INSPECTION :- When there is a regularity and homogeneity in the series
then there is a single mode which can be located at a glance by looking into the
frequency column for having maximum frequency.
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11.  ILLUSTRATION (1)
Find mode from the following series;-
Height (in cm) no. of person
150 2
160 4
170 8
180 10
190 6
200 5
210 3
Solution :- by inspection of the frequency it is noted that the maximum
frequency is 10 which corresponds to the value 180 hence mode is 180 cm.
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12. 2. BY GROUPING METHOD :-
 When there are irregulation in the frequencies increase or decrease in hapharard
way or two or more frequencies are equal then it is not obvious that which one is
the maximum frequency.
 In such case we use the method of grouping to decide which one maybe
considered as maximum frequency .
 That is we try to find out single mode by using grouping method .
 This method involve the following steps .
a. PREPARE GROUPING TABLE
b. PREPARE ANALYSIS TABLE
c. FIND MORE
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13. a. FOR PREPRING A GROUPING TABLE WE PROCEED AS
FOLLOWS :-
 COLUMN 1. - given frequencies
 COLUMN2 . - given frequency are added in two’s
 COLUMN3.- the given frequencies are added in two’s living out the first
frequency
 COLUMN4. - the given frequencies are added in three’s
 COLUMN5.- the given frequencies are added in three’s living out the first
frequency
 COLUMN6. – the given frequency are added in three’s living out the first two
frequencies.
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14. b. CONSTRUCTION OF ANALYSIS TABLE :- The value containing the
maximum frequency are noted down for each column and are written in a table
called analysis table.
c. LOCATION OF MODE :- The value of the variable which occurs maximum
number of time in the analysis table is called mode.
ILLUSTRATION (2) :- Calculate mode from following series ;-
X = 12, 13 , 14 , 15, 16 , 17, 18
F = 2 , 10, 3, 8, 9, 8, 7
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15. GROUPING TABLE
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16. ANALYSIS TABLE
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Mode = 16

17.  The process of computing mode in case of a grouped series or grouped
frequency distribution with the help of formula involves the following steps;-
1. Determine the modal class ( in exclusive forms). The class having the
maximum frequency is called modal class . this is done either by inspection or
by grouping method.
2. Determine the value of mode by applying the formula;-
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18.  ILLUSTRATION (1)
The distribution wages in a factory is as follows , calculate the mode ; -
WAGES(IN RS) NO. OF WORKERS
0 – 10 6
10 – 20 9
20 – 30 10
30 – 40 16
40 – 50 12
50 – 60 8
60 – 70 7
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19. Solution :- by inspection the maximum frequency is 16 hence the modal class
is (30-40) .
f0 = frequency of the pre modal class (20 – 30) = 10
f1 = frequency of the modal class (30 – 40) = 16
f2 = frequency of the subceeding modal class (40 – 50) = 12
L2 = 40 , L1 = 30
Formula :-
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20. Z = 30 + 16 – 10 ( 40 - 30)
2×16 -10 -12
Z = 36
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Mode is 36

21.  It is readily comprehensible and easily understood .
 It is easy to calculate . in some cases it is located by inspection.
 It is not affected by extreme values, provided they do not have maximum
frequency.
 It can be very easily determine from graph .
 It can be calculate with open and class – interevals.
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22.  It is ill defined.
 It is indefinite and indeterminate and in some cases impossible to find a definite
value.
 It is not based on all observations. So it may not be a good representative.
 It is not capable of further algebraic treatment.
 Sometimes there can be more than and mode and sometime there is no mode in
the data.
 As compared to mean , it is affected to a greater extent by fluctuations of
sampling.
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23. When a quick and approximate measure of central tendency is desired.
When the measure of central tendency should be the most typical value.
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 Dr. S. M. Shukla Business Statistics

25.  Dr. S. M. Shukla Business Statistics